In a family there are two cars. The sum of the ...

32.05 average for both?  am I close?

This is not the best worded problem I have ever heard, but, I think I understand, maybe;

since they got 65 mpg together, car A gets y mpg and car B gets 65 - y mpg.  We can assign the gals used to either to determine the value of "y" , so   

65-y X 30 +  y X 40 = 2200

1950 - 30y + 40y = 2200

10y = 250

y = 25

65 - 25 = 40 

so one car gets 25 mpg aver. and the other gets 40 mpg aver.  which gives us the totaled average of 65

to check to see if these numbers will work :  go back to original equation

65-y X 30 +  y X 40 = 2200

65 - 25 X 30 = 40 X 30 = 1200

25 X 40 = 1000

1000 + 1200 = 2200

m/40 +(2200 - m)/30 = 65, where m is first car mileage.

Multiply through by 120

3m + 4(2200 - m) = 7800

m = 8800 - 7800 = 1000 miles

Second car does 2200 - 1000 = 1200

Check: 1000/40 +1200/30 = 25 + 40 = 65

Regards - Ian